Question: The diffusion equation c/t = D 2 c/x 2 where D is a positive constant, describes the diffusion of heat through a solid, or

The diffusion equation

∂c/∂t = D ∂²c/∂x²

where D is a positive constant, describes the diffusion of heat through a solid, or the concentration of a pollutant at time t at a distance x from the source of the pollution, or the invasion of alien species into a new habitat. Verify that the function

с (х, t) У4пDi e-x³/(4Dn)

is a solution of the diffusion equation.

(, t) 4Di e-x/(4Dn)

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cx t Thus c t 1 4T Dt t c x 2c x 4Dt 1 e4Dt x14Dt 4D 4Dt 4Dt ... View full answer

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